While the effect of rotation on spectral lines is complicated in rapidly-rotating stars because of the appreciable gravity-darkening effect differing from line to line , it is possible to make use of this line-dependent complexity to separately determine the equatorial rotation velocity ( v _ { e } ) and the inclination angle ( i ) of rotational axis .
Although line-widths of spectral lines were traditionally used for this aim , we tried in this study to apply the Fourier method , which utilizes the unambiguously determinable first-zero frequency ( \sigma _ { 1 } ) in the Fourier transform of line profile .
Equipped with this technique , we analyzed the profiles of He i 4471 and Mg ii 4481 lines of six rapidly-rotating ( v _ { e } \sin i \sim 150–300 km s ^ { -1 } ) late B-type stars , while comparing them with the theoretical profiles simulated on a grid of models computed for various combination of ( v _ { e } , i ) .
According to our calculation , \sigma _ { 1 } tends to be larger than the classical value for given v _ { e } \sin i .
This excess progressively grows with an increase in v _ { e } , and is larger for the He line than the Mg line , which leads to \sigma _ { 1 } ^ { He } > \sigma _ { 1 } ^ { Mg } .
It was shown that v _ { e } and i are separately determinable from the intersection of two loci ( sets of solutions reproducing the observed \sigma _ { 1 } for each line ) on the v _ { e } vs . i plane .
Yet , line profiles alone are not sufficient for their unique discrimination , for which photometric information ( such as colors ) needs to be simultaneously employed .